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lfunc_lfunctions • Show schema
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{'Lhash': '719657613896140177816666305192', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 3.1462643699419726], 'a6': [0, 0], 'a7': [0, -3.449489742783178], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.798149469277257, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1728.1727', 'coefficient_field': 'CDF', 'conductor': 1728, 'conductor_radical': 6, 'conjugate': '1690125362701311112957399600022', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -3.1462643699419726], [-5.0, 0]], [[1.0, 0], [0, 3.449489742783178], [-7.0, 0]], [[1.0, 0], [4.5604779323150675, 0], [11.0, 0]], [[1.0, 0], [-6.898979485566356, 0], [13.0, 0]], [[1.0, 0], [0, -3.4641016151377544], [-17.0, 0]], [[1.0, 0], [0, -4.898979485566356], [-19.0, 0]], [[1.0, 0], [2.8284271247461903, 0], 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'5.53178914149489442237267755547465', '6.58361082167563346850313676004458', '7.88629393262715403277456088972854', '8.459099993455520483534416973836680', '8.989028221279246306259444890112637'], 'prelabel': '2-12e3-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.714586042788248, 'root_angle': -0.25, 'root_number': '0.e-55 - 1.0000000000000000000000000000000000000000000000000000000*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.56770975674730254520479892569', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.97001597124107924997606638913', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.99964976748049310157864451397', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.798149469277257, 'bad_primes': [2, 3], 'central_character': '12.11', 'conductor': 1728, 'conductor_radical': 6, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1728/2/c/g/1727/7'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-12e3-12.11-c1-0-8', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-12e3-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.714586042788248, 'root_angle': -0.25, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.56770975674730254520479892569', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '719657613896140177816666305192', 'Lhash_array': ['719657613896140177816666305192'], 'factors': ['2-12e3-12.11-c1-0-8'], 'label': '2-12e3-12.11-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1728/2/c/g/1727/7'}